In recent years there has been a growth in interest in studying the heart from the perspective of the physical sciences: mechanics, fluid flow, electromechanics. This volume is the result of a workshop held in July 1989 at the Institute for Nonlinear Sciences at the University of California at San Diego that brought together scientists and clinicians with graduate students and postdoctoral fellows who shared an interest in the heart. The chapters were prepared by the invited speakers as didactic reviews of their subjects but also include the structure, mechanical properties, and function of the heart and the myocardium, electrical activity of the heart and myocardium, and mathematical models of heart function.

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1 Structure and Function of the Diastolic Heart.- 1.1 Introduction.- 1.2 The Microstructure of the Heart.- 1.3 Mechanical Properties of Myocardium.- 1.4 Concluding Remarks.- References.- 2 Structural Considerations in Formulating Material Laws for the Myocardium.- 2.1 Introduction.- 2.2 Structural Background.- 2.3 Formulation of Stress-Strain Relations.- 2.4 Simulation of a Ventricular Wall Segment Subjected to Various Loading Conditions.- 2.5 Discussion.- References.- 3 Toward a Stress Analysis in the Heart.- 3.1 Introduction.- 3.2 Quantifying Material Properties.- 3.3 Characteristics of Cardiac Tissue.- 3.4 A Myocardial Constitutive Determination.- 3.5 Stress Analysis.- 3.6 Conclusions.- References.- 4 Identification of the Time-Varying Properties of the Heart.- 4.1 Introduction.- 4.2 Theory.- 4.3 Apparatus.- 4.4 Method.- 4.5 Results.- 4.6 Discussion.- References.- 5 Factors Affecting the Regional Mechanics of the Diastolic Heart.- 5.1 Introduction.- 5.2 The Left Ventricular Pressure-Volume Relation.- 5.3 Regional Ventricular Function.- References.- 6 Finite Element Modeling of Ventricular Mechanics.- 6.1 Introduction.- 6.2 The Finite Element Method.- 6.3 An Axisymmetric Finite Element Model of the Passive Left Ventricle.- References.- 7 Multidimensional Measurement of Regional Strains in the Intact Heart.- 7.1 Introduction.- 7.2 Strain Analysis.- 7.3 Finite Strains in the Normal Heart.- 7.4 Abnormal Finite Strains: Ventricular Pacing and Acute Ischemia.- References.- 8 Epicardial Deformation From Coronary Cinéangiograms.- 8.1 Introduction.- 8.2 Data Acquisition.- 8.3 Static Surface Estimation.- 8.4 Motion from Bifurcations.- 8.5 Motion from Vessels.- 8.6 Discussion.- References.- 9 Functional Consequences of Regional Heterogeneity in the Left Ventricle.- 9.1 Left Ventricular Heterogeneity Under Physiologic Conditions.- 9.2 Potential Mechanisms for Regional Heterogeneity in Deformation.- 9.3 Functional Consequences of Regional Heterogeneity.- 9.4 Theoretical Models of Regional Heterogeneity.- References.- 10 Mathematical Modeling of the Electrical Activity of Cardiac Cells.- 10.1 Introduction.- 10.2 Ionic Models Using the Hodgkin-Huxley Formulation.- 10.3 Background Currents.- 10.4 Activation.- 10.5 Inactivation.- 10.6 Pump and Exchange Currents.- 10.7 Applications of Ionic Models.- 10.8 Reduced Ionic Models.- 10.9 Single Channel Models.- 10.10 Single Channel Dynamics: Stochastic or Deterministic?.- References.- 11 Mathematical Models of Pacemaker Tissue in the Heart.- 11.1 Introduction.- 11.2 Modeling Aspects.- 11.3 The Bullfrog Sinus Venosus Pacemaker Cell.- 11.4 The Bullfrog Atrial Cell.- 11.5 The ACh-Sensitive K+ Current IK,ACh.- 11.6 Parasympathetic Control of the Rabbit SA Node Cell.- 11.7 Rabbit Atrial Cell Model.- 11.8 Modeling Nodal Regions.- 11.9 Summary.- References.- 12 Low-Dimensional Dynamics in the Heart.- 12.1 Introduction.- 12.2 Basic Concepts in Nonlinear Dynamics.- 12.3 A Topological Model of Cardiac Oscillators.- 12.4 Periodic Stimulation of Limit Cycle Oscillators.- 12.5 Stimulation of the Poincaré Oscillator at a Fixed Delay after an Action Potential.- 12.6 Periodic Stimulation of Excitable, Nonoscillating Cardiac Tissue.- 12.7 Applications and Limitations.- References.- 13 Iteration of the Human Atrioventricular (AV) Nodal Recovery Curve Predicts Many Rhythms of AV Block.- 13.1 Introduction.- 13.2 Derivation of the 1-Dimensional Map.- 13.3 Results of Iteration of the Map.- 13.4 Comparison with Clinical and Experimental Findings.- 13.5 Appendix.- References.- 14 Ionic Basis of the Wenckebach Phenomenon.- 14.1 Introduction.- 14.2 AV Nodal Wenckebach.- 14.3 Wenckebach in the Sucrose Gap.- 14.4 Wenckebach in the Ventricular Myocyte.- 14.5 Simulating Wenckebach in the Beeler and Reuter Model.- 14.6 The Recovery Curve.- 14.7 Ionic Mechanisms of Wenckebach Periodicity.- 14.8 Analytical Model of Wenckebach Periodicity.- 14.9 Conclusion.- References.- 15 Parasystole and the Pacemaker Problem.- 15.1 Introduction.- 15.2 The Pacemaker Problem.- 15.3 Dynamics of Pure Parasystole.- 15.4 Clinical Observations of Parasystole.- 15.5 Implications of Parasystole for Theory.- References.- 16 Electrical Propagation in Distributed Cardiac Tissue.- 16.1 Introduction.- 16.2 Passive Properties.- 16.3 Propagation in One Dimension.- 16.4 Propagation in Two Dimensions.- 16.5 Summary.- References.- 17 Wave Propagation in Myocardium.- 17.1 Introduction.- 17.2 The Nagumo Equation.- 17.3 Traveling Wave Solutions.- 17.4 Continuous Cable Theory.- 17.5 Discrete Cable Theory.- 17.6 A Modified Cable Theory.- 17.7 Comparison with Experiments.- 17.8 Discussion.- References.- 18 Cellular Automata Models of Cardiac Conduction.- 18.1 Introduction.- 18.2 CAMCC.- 18.3 Relation to Other Processes.- 18.4 Representing Conduction Physiology.- 18.5 Representing the Reentrant Core.- 18.6 Rationale for Interpretation of Lattice Structure.- 18.7 Spatial Variation in Conduction Physiology.- 18.8 Dynamical Inhomogeneities in Conduction Physiology.- 18.9 Conclusion.- References.- 19 Estimating the Ventricular Fibrillation Threshold.- 19.1 Introduction.- 19.2 The Continuum Approximation.- 19.3 The Diffusion Coefficient of Electric Potential.- 19.4 The Stimulation Threshold.- 19.5 Minimum-Energy Ventricular Pacing.- 19.6 The Ventricular Fibrillation Threshold.- 19.7 Vulnerable Period Duration.- 19.8 The Upper Limit of Vulnerability.- 19.9 Minimum-Energy Defibrillation.- 19.10 Transition from Reentrant Tachycardia to Turbulence.- 19.11 Conclusion.- References.- 20 Basic Mechanisms of Ventricular Defibrillation.- 20.1 Introduction.- 20.2 Location of Earliest Activation Following Failed Defibrillation Shocks.- 20.3 Origin of Activation after Unsuccessful Defibrillation Shocks.- 20.4 The Upper Limit of Vulnerability.- 20.5 The Upper Limit of Vulnerability Hypothesis for Defibrillation.- 20.6 Electrical Initiation of Ventricular Fibrillation.- 20.7 The Critical Point and the Upper Limit of Vulnerability.- 20.8 The Critical Point and the Probability Function of Defibrillation.- 20.9 Very High Potential Gradients Have Detrimental Effects on the Heart.- 20.10 The Mechanism of Defibrillation.- References.- 21 Mechanically Induced Changes in Electrophysiology: Implications for Arrhythmia and Theory.- 21.1 Introduction.- 21.2 Experimental Evidence for Mechanoelectric Feedback.- 21.3 Mechanism of Mechanoelectric Feedback.- 21.4 Mechanoelectric Feedback and Arrhythmia: General Considerations.- 21.5 Mechanoelectric Feedback and Arrhythmia: Clinical Considerations.- 21.6 Theoretical Implications.- 21.7 Summary.- References.- 22 Nonlinear Dynamics at the Bedside.- 22.1 Nonlinear Hearts.- 22.2 Dynamical Deceptions.- 22.3 The Prognosis For Nonlinear Science in Clinical Cardiology.- References.- 23 A Clinical Perspective on Theory of Heart.- 23.1 Introduction.- 23.2 Present Impact on Theory in the Clinical Arena.- 23.3 Future Considerations.- 23.4 Conclusion.- References.